FUNCTION: FM_n - fix the number of variables

CALLING SEQUENCE:

FM_n(n)

FM_n(n, 'load')

FM[FM_n](n)

FM[FM_n](n, 'load')

PARAMETERS:

n = any positive integer

SYNOPSIS:

• The FM_n function is used to fix the number of variables. This value is stored in the _FMn global variable. The ring of polynomials in x1,...,xn, where n=_FMn, will be considered as a free-module over the ring of symmetric polynomials in x1,..., xn, with basis the Schubert polynomials indexed by permutations in the symmetric group S(n).

• When called without any argument, it returns the current value of _FMn.

• When called with a second paramater 'load', it loads all pre-computed tables of available data for the given n. If one table is not available, it computes it so that it can take some time.

• Whenever there is a conflict between the function name FM_n and another name used in the same session, use the long form FM['FM_n'].

EXAMPLES:

> with(FM):
> FM_n();
 
                                      4
 
> FM_n(3, 'load');
 
                                      3